Symbolic Toolbox: integration
显示 更早的评论
>> int('cos(x^2)^2')
Warning: Explicit integral could not be found.
ans =
int(cos(x^2)^2, x)
>> int('cos(2*x^2)')
ans =
(pi^(1/2)*fresnelC((2*x)/pi^(1/2)))/2
But there is a formula cos(2y)=2cos(y)^2)-1 and in first case MATLAB can't solve..
May be MuPAD forced to solve?
9 个评论
Walter Roberson
2011-12-12
It works in Maple.
Walter Roberson
2011-12-13
You could _try_
int(simple('cos(x^2)^2'),'x')
Andrei Bobrov
2011-12-13
Hi Walter! Small typo:
int(simplify('cos(x^2)^2'),'x')
Walter Roberson
2011-12-13
No, simple() is correct rather than simplify() . simple() goes through a variety of conversions to find the "best" one, telling you along the way what it is doing.
Andrei Bobrov
2011-12-13
in "my" MATLAB with Maple Toolbox
http://imageshack.us/photo/my-images/838/symint.png/
Andrei Bobrov
2011-12-13
in "my" MATLAB with MuPAD (I use MATLAB 7.10)
http://imageshack.us/photo/my-images/542/symint2.png/
Walter Roberson
2011-12-13
int(simple(sym('cos(x^2)^2')),'x')
Andrei Bobrov
2011-12-13
I'm agree , Walter!
(Maple Toolbox)
http://imageshack.us/photo/my-images/843/symint3.png/
Andrei Bobrov
2011-12-13
Last comment :)
http://imageshack.us/photo/my-images/402/symint4.png/
(for Maple Toolbox)
采纳的回答
bym
2011-12-14
Apparently you have to do the substitution manually
int(simple(cos(x^2)^2))
Warning: Explicit integral could not be found.
Using the sincos version returned by
simple(cos(x^2)^2)
yields this
int(cos(2*x^2)/2 + 1/2)
ans =
x/2 + (pi^(1/2)*fresnelC((2*x)/pi^(1/2)))/4
I could not find where the sincos 'simplification' is available outside the simple command as it is in Maple...maybe this is the reason Maple returns the result automagically ;)
[edit for completeness]
int(feval(symengine, 'combine', cos(x^2)^2, 'sincos'))
ans =
x/2 + (pi^(1/2)*fresnelC((2*x)/pi^(1/2)))/4
4 个评论
Walter Roberson
2011-12-14
http://www.mathworks.com/help/toolbox/mupad/stdlib/combine.html
combine(cos(x^2)^2,sincos)
Note that this is at the MuPAD level, not the MATLAB level, so you may need to use feval() or similar to access it
feval(symengine, 'combine', cos(x^2)^2, 'sincos')
bym
2011-12-14
works well, my local documentation does not turn up an obvious help topic when searching for 'combine'
feval(symengine, 'combine', cos(x^2)^2, 'sincos')
ans =
cos(2*x^2)/2 + 1/2
thanks Walter
Igor
2011-12-14
Walter Roberson
2011-12-14
Humans are better at seeing patterns or understanding context than machines are. It is *often* the case that a human will have to apply knowledge of theoretical equivalences in order to make progress in integration.
MuPAD is not as strong as some of the other products around, but _all_ of them are missing a lot of patterns.
更多回答（0 个）
类别
在 帮助中心 和 File Exchange 中查找有关 Common Operations 的更多信息
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!
Translated by 
